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以非局部弹性理论为基础,采用欧拉-伯努利梁模型,考虑了管型区域内滑移边界条件以及碳纳米管的小尺度效应,应用哈密顿原理获得轴向磁场中磁敏载流单壁碳纳米管(SWCNT)的振动控制方程以及边界条件;依靠微分变换法(DTM)对此高阶偏微分方程进行求解,通过数值计算研究了单壁固支载流碳纳米管的振动与失稳问题。结果表明:轴向磁场强度H_x、克努森数K_n、小尺度参数m都会对系统振动频率以及系统稳定区域产生影响,其中K_n及m越大,系统基频越低,稳定区域越小;而当外加轴向磁场强度达到一定数值后,磁场作用将使系统的稳定性明显加强。
Based on the non-local elastic theory, the Euler-Bernoulli beam model is used to consider the slip boundary conditions in the tube region and the small-scale effect of the carbon nanotubes. The magnetic field-sensitive current carrying capacity Single-walled carbon nanotubes (SWCNT) vibration control equations and boundary conditions; relying on differential transformation (DTM) to solve this high-order partial differential equations, numerical simulation of single-walled carbon nanotubes supported stationary flow and Instability problem. The results show that the axial magnetic field strength H_x, the Knudsen number K_n and the small-scale parameter m all affect the system vibration frequency and the stability of the system. The larger the K_n and m are, the lower the fundamental frequency is, and the stable area is smaller. When the applied axial magnetic field strength reaches a certain value, the magnetic field will make the system stability significantly enhanced.